Barrow Wights just means barrow men. Prior to Tolkien, their was no connection between the word "wight" and undead. The Barrow Wights are described by Tolkien as evil spirits that entered the Barrows of old kings in order to defile them, not the reanimated bodies of the kings themselves, so their "undead" status is open to question.

The only 100% certifiable undead are the Dead Men of Dunharrow, and they are spirits, who (it is speculated in the book) have no power to physically harm the living. A Far Dragon is the best kind...